What are the origins of the expression "mea culpa, mea culpa, mea culpa". I have heard one of my past math professors say this, and was wondering.
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Mea culpa comes from the Confiteor which is a common prayer recited, among other times, towards the end of the prayers at the foot of the altar in the (Catholic) Roman rite.
The full text of the prayer as recited in the Tridentine missal:
Confiteor Deo omnipotenti, beatæ Mariæ semper Virgini, beato Michaeli Archangelo, beato Ioanni Baptistæ, sanctis Apostolis Petro et Paulo, omnibus Sanctis, et vobis, fratres: quia peccavi nimis cogitatione, verbo et opere: mea culpa, mea culpa, mea maxima culpa. Ideo precor beatam Mariam semper Virginem, beatum Michaelem Archangelum, beatum Ioannem Baptistam, sanctos Apostolos Petrum et Paulum, omnes Sanctos, et vos, fratres, orare pro me ad Dominum Deum nostrum.
This is usually translated as: through my fault, through my fault, through my most grievous fault.
Note that mea culpa is in the ablative, answering the question of "in what way" once has sinned (peccavi).
The phrase mea culpa (along with other variants, including the one you cited) has passed into colloquial speech and, at least in my experience, has become a slightly tongue-in-cheek way of saying, "My bad."